If you count the bolts on the transmission pan that would tell me what kind you have. Or the shape. The 400 has 13 bolts and the 4l80 had 17 if I remember.
Guessing its 4L80E. As far as putting a few quarts in and driving, that depends on the amount it leaks. If there is any doubt in your mind, put it on the hook especially if you have no cost towing.
And personally I would be there for the whole repair, I would ask to check wear on driveshaft yoke and bushing in the housing and show you. You can tell if its bad by running you finger across it, it will have a noticeable ridge.
If they just pull the driveshaft off take old seal out with screwdriver, then 500 is way way too high, and only putting bandaid on problem that will come back.
Just did a quick internet search, found a tail housing kit for 30 bucks on Ebay including bushing and seal and gasket... :-)